Mr. Elefante, the family’s lead trustee and a Dow Jones board member, will play a crucial role. Mr. Elefante sits on most of the family’s key trusts, and a number of family members have relied on his counsel in forming their own opinions on the offer. Mr. Elefante and a Hemenway & Barnes colleague, Kurt F. Somerville, are the only trustees on one of the family’s biggest trusts.

Indeed, Mr. Elefante has told board colleagues he can deliver a little less than half of the family’s 64% stake. That rough one-third of the company’s voting power likely would be enough to cement a sale to Mr. Murdoch. That is because some 29% of the total voting power of the company rests in the hands of non-Bancrofts. Almost all of these holders, many of them arbitragers, are expected to support the deal.

Only 51% of the voting power is required for approval, but News Corp. will need to leave itself some extra margin, given a chunk of shares typically remain unvoted in merger situations.

News Corp. owns more than 100 papers in Australia, Britain, the U.S., Fiji and Papua New Guinea; Twentieth Century Fox Film; the Fox TV network; HarperCollins Publishers and the popular MySpace Internet site.